UNIVERSAL APPLICATION OF FOURIER SERIES IN ENGINEERING, MEDICINE, AND ECONOMICS

Abstract

In today’s era of digital technologies, signal and image processing is widely applied in various fields such as medicine, communications, audio and video technologies, artificial intelligence, and engineering. In these processes, Fourier analysis—namely, Fourier series and integral transforms—serves as one of the fundamental mathematical tools for analyzing the composition of signals and images, compressing them, and filtering noise. With the help of Fourier series and transforms, complex functions can be decomposed into sine and cosine waves, which facilitates easier analysis, noise reduction, and data compression. This article provides a detailed analysis of the fundamental concepts of Fourier series and transforms, their mathematical foundations, and their practical applications across various fields.